Spatiotemporal Dynamics for a Diffusive Predator-Prey Model with Nonlocal Competition in a Circular Domain

Within a circular symmetric domain, we investigate the corresponding dynamic behaviors of a reaction-diffusion predator-prey system with nonlocal competition. First, sufficient conditions for the local stability of the steady state are established and criteria for the occurrence of various bifurcations are derived. Furthermore, based on the center manifold method and normal form theory, the third order normal form formula for the Turing-Hopf bifurcation is refined, which adapts to the systems with nonlocal competing terms of a wide class of kernel functions in principle in a circular domain. Finally, a series of numerical simulations are performed to validate the analytical results and visually illustrate the rich spatiotemporal patterns by nonlocal competition.